The object of this work is to employ Mossbauer spectroscopy and susceptometry in the examination of hemoproteins and their synthetic analogues. The Mossbauer apparatus is in place and operating. The susceptometer has settled what we regarded as the interesting question at room temperature. We have delayed its conversion to low temperatures because of the presence of other work and the availability of susceptibility data from our chief collaborator. We are steadily adding to our array of computer techniques and programs for theoretical interpretation of Mossbauer and susceptibility data. Our method of operation has been to keep several projects going, and concentrate effort on the area which at the time is ripe for exploitation. We have recently successfully interpreted several synthetic hemes which crystallize as dimers with interheme spin coupling. This area is currently ripe for exploitation. Many of the experimental results which we now understand in terms of spin coupling have been in hand for several years and have received much unsuccessful theoretical effort on our part. Our understanding of one case of heme-heme spin interaction is confirmed by a wealth of experimental detail. A second case, with iron-radical interaction as an added complication, is also understood. Some additional cases of intermolecular coupling of quantum mechanically mixed spin ions seem to be working out as well. We intend to investigate more such systems in order to confirm our present interpretations and develop systematic correlation of the spin coupling parameters and structure. In view of the presence of spin coupling within important hemoprotein enzymes, this is obviously of biological relevance. We also have in reserve some now-familiar but still vexing problems in which the fortunate break has not yet come. Our past interpretations of deoxyheme electronic structure need refinement, and work on a series of synthetic 5-coordinate ferrous hemes has begun. We remain not completely satisfied by the Maltempo quantum mixed spin model. The nature of the low excited states of oxyhemes remains unclear. An understanding of the function of heme proteins is important because they are essential features of almost all living organisms. The long-range relevance to health problems is well established.